Unusual Matrix

2000ms

262144K

Description:

You are given two binary square matrices $$$a$$$ and $$$b$$$ of size $$$n \times n$$$. A matrix is called binary if each of its elements is equal to $$$0$$$ or $$$1$$$. You can do the following operations on the matrix $$$a$$$ arbitrary number of times (0 or more):

vertical xor. You choose the number $$$j$$$ ($$$1 \le j \le n$$$) and for all $$$i$$$ ($$$1 \le i \le n$$$) do the following: $$$a_{i, j} := a_{i, j} \oplus 1$$$ ($$$\oplus$$$ — is the operation xor (exclusive or)).
horizontal xor. You choose the number $$$i$$$ ($$$1 \le i \le n$$$) and for all $$$j$$$ ($$$1 \le j \le n$$$) do the following: $$$a_{i, j} := a_{i, j} \oplus 1$$$.

Note that the elements of the $$$a$$$ matrix change after each operation.

For example, if $$$n=3$$$ and the matrix $$$a$$$ is: $$$$$$ \begin{pmatrix} 1 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix} $$$$$$ Then the following sequence of operations shows an example of transformations:

vertical xor, $$$j=1$$$. $$$$$$ a= \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix} $$$$$$
horizontal xor, $$$i=2$$$. $$$$$$ a= \begin{pmatrix} 0 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 0 \end{pmatrix} $$$$$$
vertical xor, $$$j=2$$$. $$$$$$ a= \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} $$$$$$

Check if there is a sequence of operations such that the matrix $$$a$$$ becomes equal to the matrix $$$b$$$.

Input:

The first line contains one integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases. Then $$$t$$$ test cases follow.

The first line of each test case contains one integer $$$n$$$ ($$$1 \leq n \leq 1000$$$) — the size of the matrices.

The following $$$n$$$ lines contain strings of length $$$n$$$, consisting of the characters '0' and '1' — the description of the matrix $$$a$$$.

An empty line follows.

The following $$$n$$$ lines contain strings of length $$$n$$$, consisting of the characters '0' and '1' — the description of the matrix $$$b$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$1000$$$.

Output:

For each test case, output on a separate line:

"YES", there is such a sequence of operations that the matrix $$$a$$$ becomes equal to the matrix $$$b$$$;
"NO" otherwise.

You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).

Sample Input:

Sample Output:

YES
YES
NO

Note:

The first test case is explained in the statements.

In the second test case, the following sequence of operations is suitable:

horizontal xor, $$$i=1$$$;
horizontal xor, $$$i=2$$$;
horizontal xor, $$$i=3$$$;

It can be proved that there is no sequence of operations in the third test case so that the matrix $$$a$$$ becomes equal to the matrix $$$b$$$.

Informação

Provedor Codeforces

Código CF1475F